Algorithmic and approximation analyses of the shorter queue model

Abstract

A system of two parallel queues where the arrivals from a single stream of customers join the shorter queue is considered. Arrivals form a homogeneous Poisson stream and the service times in each of the two queues are independent exponential variates. By treating one of the queues as bounded, the steady‐state probability vector for the system can be expressed in a modified matrix‐geometric form and can be computed efficiently. Computational procedures for the sojourn time distribution and characteristics of the departure stream are developed. Some numerical results are presented, and based on these results an efficient approximation scheme for the model is developed which can be readily extended to systems with more than two parallel queues.

Bounds for performance characteristics: a systematic approach via cost structures

“…Exact analytical results can be found in 13, 7, 1]. There are also many papers analyzing approximations for the shortest queue problem, see 6,8,9,10,11,15,16,18,27]. It appears that the present approach leads to several models producing bounds for performance characteristics such as, e.g., the mean waiting time.…”

“…These models cover the ones in 6,9,10,18,27]. None of these references, however, rigorously proves that these models indeed produce bounds.…”

Flexible Assembly and Shortest Queue Problems

“…Also the number of numerical approaches is rather restricted. We might mention here a paper of Grassmann ([13]) and a paper by Rao and Posner ( [18]), both based on approximating models.…”

Bad luck when joining the shortest queue

“…The efficiency of the algorithm is further enhanced in Blanc (1993). Other approaches to shortest-queue systems can be found, among others, in Haight (1958), Flatto and McKean (1977), Halfin (1985), Rao and Posner (1987), Hanqin and Rongxin (1989), Adan, Wessels and Zijm (1990), Adan, Van Houtum and Van der Wal (1994) and Wu and Posner (1997). Winston (1977), Johri (1989) and Hordijk and Koole (1990) consider the optimality of the shortest queue discipline.…”